Deformed Kac-Moody algebras and their representations
type: Item
instance of: scholarly article
title: Deformed Kac-Moody algebras and their representations
zbMATH Open document ID: 1192.17011
author: Jianbo Liu
author: Kaiming Zhao
published in: Journal of Algebra
publication date: 2008-07-29T00:00:00Z
review text: For any generalized Cartan matrix \(A\), the authors introduced the Lie algebra \(\mathfrak{G}(A)\). This algebra, a generalization of nondegenerate Lie algebras was investigated by many other authors recently, and can also be regarded as a certain deformation of Kac-Moody algebras. Therefore, similar methods can be used to study the structure and representation theory of this algebra. In the present paper, the lowest weight modules and the highest weight modules are described, and some better results are obtained in the case of the symmetrizable \(A\).
Mathematics Subject Classification ID: 17B65
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17B67
zbMATH DE Number: 5304630
zbMATH Keywords: deformed Kac-Moody algebra
zbMATH Keywords: invariant symmetric bilinear form
zbMATH Keywords: highest weight module
zbMATH Keywords: irreducible module
reviewed by: Xiandong Wang
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2008.01.009
OpenAlex ID: W2020221683
cites work: Indefinite Kac-Moody algebras of classical type
cites work: Q5687442
cites work: Q4280747
cites work: Introduction to Lie Algebras and Representation Theory
cites work: Q3693664
cites work: Q4008275
cites work: Classification of finite-dimensional solvable Lie algebras with nondegenerate invariant bilinear forms
cites work: Isomorphisms of Upper Cartan-Matrix Lie Algebras
cites work: Q5691063
cites work: Q4003729
cites work: A class of non-degenerate solvable Lie algebras and their derivations
DOI: 10.1016/J.JALGEBRA.2008.01.009
description: scientific article; zbMATH DE number 5304630